With Liverpool, Suarez had to pretty much carry the whole team each and every game. He had to play with the likes of Poulsen, Konchesky, Spearing, Adam, Downing, Allen, Carroll, etc. week in week out. In several games, he'd work extremely hard to score a goal only for the inept defenders to concede moments later. I think a lot of world-class players would lose their cool from time to time had they been made to constantly carry mediocre players in a mid-table team with the national media doing their best to get rid of you.
I remember a Europa League game where Liverpool had to score 3 goals at home against Zenit to move into the semi-finals. Suarez played out of his skin to score 2 wonderful goals and yet was let down again by his team conceding a goal early and they were knocked out. He was in tears that night. The only other game I saw him cry was the Crystal Palace game last season where his team managed to concede 3 goals in less than 15 minutes, throwing away their 3-0 lead and ending any hope of winning the PL title then and there.
With Barca that pressure is pretty much gone, or at least reduced by a huge amount. Not claiming that he won't lose his cool again, but I feel that now he no longer needs to push himself to the brink of insanity to achieve something. The weight of the team doesn't rest squarely on his shoulders anymore, and so maybe just maybe we won't see him lose his head like previously from here on out.
